My experience of Big Co is that you have both a manager (HR and business sense) and a supervising/lead engineer (SDE 3) for a product.

I don’t think I explained that well — but a 3:3:1 to 5:5:1 SDE 1:2:3 mix is fairly standard across industry. (Again, with an SDM doing the managing.)

I used the word “supervising” because I wanted to distinguish that technical leadership from managing, but didn’t explain enough. Sorry for the confusion.